Endogenous Altruism in Buyer-Seller Relations and itsImplications for Vertical Integration ∗

Julio J. Rotemberg

This draft: October 8, 2006

Abstract

This paper considers a standard buyer-seller relation where the seller can take non-contractible actions that raise the value of the good to the buyer. This relationshipcan either take place inside a firm - so that the buyer can give orders to the seller -or across firm boundaries. Both the buyer and the seller can, if they wish, becomealtruistic towards one another. Becoming altruistic is costly and leads individuals tocare about the other individual’s payoffs ex post. Still, its observability can lead it toarise endogenously in buyer-seller transactions. Under plausible conditions, altruismfrom seller to buyer arises more easily for outside contractors than for employees. Theresult is that endogenous altruism can be a force that leads to disintegration. Altruismfrom buyers to their supplying contractor can also arise. As suggested by the empiricalliterature, it increases the frequency of purchases. (JEL: D2, L2)

∗Harvard Business School, Soldiers Field, Boston, MA 02163. Email: jrotemberg@hbs.edu. I wish tothank George Baker, Bob Gibbons, Oliver Hart, Ramon Casadesus Masanell and Rakesh Khurana for helpfulconversations.

Sociologists of organizations such as Granovetter (1985) and Uzzi (1997) have emphasized

that many economic transactions are “embedded” in social relations or, more particularly,

are carried out between personal friends. Uzzi (1997), for example, contains vivid descrip-

tions of friendship between executives at apparel “manufacturers” (buyers) and executives

at “contractors” (the firms that actually make the garments).1 Friendship ties also exist

within firms, though frequency of interactions at work is only loosely relate to the strength

of these ties,2 and I am not aware of any study showing warm feelings between people en-

gaged in transactions across the divisions of a single firm. There is, by contrast, evidence

that many inter-divisional transactions occur in an atmosphere of conflict and acrimony.

Eccles and White (1988) give several examples of this conflict and say that, as a result of it

“Most managers interviewed in the field study expressed the view that internal transactions

were more difficult and costly than external ones” (p. S40). They quote one manager as

saying “The internal guy, whether as supplier or as user, is never treated as well” (p. S47)

and discuss a case in the semiconductor industry where “both buyer and seller would have

preferred external transactions” (p. S43).3

Inspired by these contrasts, this paper studies conditions under which altruism is more

likely to arise between people engaged in transfer of goods and services across firms than

in similar transfers between people transacting within a firm. In this formulation, altruism

captures a particular element of friendship, namely the tendency to provide more help to

friends than to others. In Uzzi (1997), for example, suppliers who have special relationships

with their customers make extra efforts to supply high quality goods. Uzzi (1997, p. 47)

describes a “special” contractor that cut a dress “to different sizes depending on the dye color

used because the dye color affected the fabric’s stretching. The manufacturer who made the

1Uzzi (1997, p. 42) quotes a manager as saying “It is hard to see for an outsider that you become friendswith these people - business friends. You trust them and their work. You have an interest in what they aredoing outside of business”

2Burt and Knez (1996) report that, when asked to name the business contact that they perceived as mostselfish and untrustworthy, 3% of the managers in their sample named someone they interacted with daily.

3These difficulties with internal transactions are reflected in Walker and Poppo’s (1991) questionnairestudy of a large buyer’s perceptions. This buyer claimed to have somewhat more difficulty reaching agreementabout the allocation of engineering and cost changes when he was dealing with an internal profit center thanwhen he was dealing with an outside supplier.

1

order didn’t know that the dress sizes had to be cut differently to compensate for the dying.

If the contractor had not taken the initiative to research the fabric’s qualities, he would have

cut all the dresses the same way - a costly mistake for the manufacturer and one for which

the contractor could not be held responsible. Both the manufacturer and the contractor

reported that this type of integration existed only in their embedded ties because their work

routines facilitate troubleshooting and their ’business friendship’ promoted expectations of

doing more than the letter of a ’contract.’ The manufacturer explained ‘When you deal with

a guy you don’t have a close relationship with, it can be a big problem. Things go wrong

and there is no telling what will happen’ ”.

Given these benefits of dealing with an altruistic supplier, one obvious question is why

firms don’t arrange matters so that all their suppliers, including their employees, are altruis-

tic. In the model I propose, where this altruism arises endogenously as in Rotemberg (1994),

the reason is that altruism has costs as well as benefits. The particular setting in which

transactions are carried out then determines whether the costs exceed the benefits or not.4

One difference between purchase transactions carried out within firms and purchase trans-

actions across firms is the ease with which the buyer can impose his own preferred changes

in his order even when friendship ties are absent. In the case of transactions within firms,

the customer can induce changes by enlisting the help of a top executive who then orders to

supplying division to make the change. As a manager in Eccles and White (1988, p. S47)

put it, “an in-house guy may say he needs more, and if he doesn’t get them he complains

to his boss.” That CEO’s sometimes order last-minute changes in the goods supplied by

their divisions is a commonplace (see Freeland 2001, p. 246 for an example from General

Motors). This capacity of managers to give orders to employees is broadly consistent with

both Simon’s (1961) and the law of agency’s distinction between employees and outside

4While not directly related to this paper because it involves friendship among managers carrying outsimilar tasks in competing organizations rather than friendship among managers that sell to one another, In-gram and Roberts (2000) provides further evidence that the nature of business transactions affects these ties.They show that friendship is more likely among managers of competing hotels, that have more opportunitiesfor enhancing each other’s performance, than among other hotel managers.

2

contractors.5

Interestingly, the law of agency also provides a reason why textbook forms of renegotiation

are often not sufficient to induce non-altruistic contractors to provide high quality goods to

buyers. Contractors who provide goods and services are covered by the uniform commercial

code. This code requires the contractor to be conscientious and “reasonable”. Moreover, the

first substantive paragraph of this code says “The effect of the provisions of this Act may be

varied by agreement, ... except that the obligations of good faith, diligence, reasonableness

and care prescribed by this Act may not be disclaimed by agreement...” This rules out

certain holdups that might otherwise lead contractors to seek quality enhancements. This

law implies that a contractor who reveals that he knows a superior way of producing a

product which does not entail important additional costs must use this superior method and

is unable to extract additional compensation by threatening to revert to the inferior method

of production.

While it might be desirable to derive this lack of price renegotiation as well as the

increased capacity of buyers to give direct orders to in-house sellers from more fundamental

assumptions, this is largely beyond the scope of this paper. Rather, the aim here is show that

the additional scope for intervention in the case of in-house supply can reduce the altruism

of in-house suppliers relative to that of external contractors. Thereby, a feature of in-house

supply that Simon (1951) regarded as having an advantage can turn into a disadvantage.

The reason altruism can be affected in this way is that these interventions reduce its value.

There is no particular reason to expect the changes demanded by buyers, which are often

made at the last minute, to be consistent with changes that an altruistic seller discovers to

be useful for raising quality. Indeed, the complications involved in making changes in highly

interdependent systems usually imply that the implementation of one change precludes the

implementation of others that were developed independently. The result is that the value of

the quality-enhancing innovation discovered by the seller is generally lower when the buyer

5The Law of Agency p. 488 states that an employee differs from other agents because an employee is“subject to control as to the manner in which he performs the acts that constitute the execution of hisagency.”

3

also has a change he would like to implement.

This has two implications, which are drawn out in propositions 2 and 3 below. First,

external contractors can expect a higher reward from becoming altruistic because their sug-

gestions are more valuable, and this means that they are more willing to incur the cost

of gaining this altruism. Second, the minimum level of altruism that is sufficient for the

contractor to offer valuable suggestions is lower than the minimum level of altruism that

is needed for the worker to do so. Thus, if smaller levels of altruism are less costly, only

external contractors become altruistic.

Friendships, and the altruism that goes with them, develop over time. I capture this in a

simple way by treating altruism as a costly investment. While this is crude, it is worth noting

that the “investment model” in social psychology predicts that friends are more committed

to one another the larger are their earlier investments in the relationship, and this model has

received support also in non-romantic relationships (Rusbult 1980). The social-psychology

literature also stresses that friendships are cemented through time-intensive activities such

as self-disclosure. A particularly relevant study is Collins and Miller (1994). They show that,

in controlled experiments, a’s disclosure of personal information to b (an activity a generally

views as costly) leads a to like b more. There are two reasons why this finding is particularly

relevant for the current paper. First, while the idea that altruism is a choice variable may

strike some readers as fanciful, the idea that people choose how much information they

disclose to others should be uncontroversial. Second, the model requires that people know

who feels altruistic towards them. The Collins and Miller (1994) evidence suggests that b

can use evidence of self-disclosure by a as indicative that b is liked by a. “Liking” need not

be identical to altruism. On the other hand Carnevale et al. (1982) show that subjects that

have been manipulated into liking an experimenter’s confederate are also more likely to help

this confederate.

The simplest model I consider has agents first determine their altruism (the investment

phase) and then having access to one potential transaction. I also consider a setting where the

purchaser buys the good repeatedly. I do this both because friendship usually develops over

4

time, so that one would expect it to be more likely to arise when interactions are repeated

and because it might be thought that this repetition obviates the need for altruism.

In the setting I consider, high quality can indeed be produced without altruism because,

as in Klein and Leffler (1981), Shapiro and Stiglitz (1984) and Baker, Gibbons and Murphy

(2001), there exist equilibria where suppliers keep quality high to ensure that they earn rents

from future sales. Altruism nonetheless ends up playing a big role. With supplier altruism,

the provision of high quality requires fewer rents because suppliers have an incentive to seek

improvements in the product. Thus, suppliers that compete in their altruism drive down the

level of rents and become altruistic in equilibrium.

Because altruistic contractors obtain larger vicarious gains from quality improvements

than altruistic workers, altruism is more effective at reducing contractor rents than worker

rents. This again provides a reason for transacting across firm boundaries. There is also

a more direct reason to expect altruism to arise only with contractors when purchases are

repeated. For a variety of reasons, it is easier to stop transacting with a contractor than

with a worker. One reason for this difference is that many laws and regulations bear on

the employment relation. Firms face firing costs for employees in many jurisdictions; even

unemployment insurance taxes are generally “experience rated” so that tax rates are higher

for employers who fire more frequently.

If is relatively difficult to fire workers, an integrated firm that can give efficient orders

to its worker may forego the mechanism that ensures high effort by promising future rents.

The reason is that these rents have to be quite large if the probability of firing is low. As

shown in Rotemberg (1991), integration may still be profitable in this case - even if it is

socially inefficient - because it avoids giving rents to a contractor. What I show here is that

this scenario is one where only contractors tend to become altruistic in equilibrium as they

compete down the flow of rents.

One problem with the equilibrium where the firm buys repeatedly from a contractor

and pays him more than his marginal cost of production is that the firm has an insufficient

incentive to make purchases. This leads to inefficiency if demand is variable and the firm

5

does not make purchases every period. A solution to this problem is for the purchaser to

become altruistic towards his contractor.

Such altruism is consistent with observations in Uzzi (1997 p.55) who reports that a man-

ufacturer who was permanently moving his operations to Asia did not disclose his proposed

move to his “arm’s-length” suppliers but personally notified his “special” contractors so they

could adapt to the loss of his business. More generally, and exactly in line with the model’s

predictions, buyers that have “special” relationships with sellers seem to try to maintain

their purchases from these sellers in downturns. As a manager told Uzzi (1997 p. 54) “when

we are not so busy, we try to find work for that time for our key contractors. We will put a

dress into work to keep the contractor going. We’ll then store the dress in the warehouse.”

Similar ideas are expressed in Lorenz (1988). He reports on close relationships among small

and medium French engineering firms, which he describes as involving two-sided trust. Ac-

cording to him, these buyers trust that the seller will produce high quality while the sellers

expect that “the client firm will make every effort to guarantee a level of work” (p. 206).

This paper is related to Kranton and Minehart (2000) who build a model where buyers

can either procure goods in-house or incur costs to establish relations with external sellers.

The models differ, however, because Kranton and Minehart (2000) suppose that the only

benefit of incurring the costs of building external relations is that external sellers are more

flexible; they can more easily redirect their output to different buyers depending on the

randomness of individual demand. With a constant level of purchases, their model implies

that internal supply is superior. Insofar as buyers succeed in keeping the level of orders

from their “key” sellers relatively stable, the Kranton and Minehart (2000) model seems

more applicable to the relationship of buyers with “arm’s-length” rather than with “special”

suppliers.

The paper proceeds as follows. Section 1 studies contractor and employee altruism in

one-shot interactions. Section 2 analyzes repeated interactions with constant demand while

Section 3 focuses on demand fluctuations and buyer altruism. Section 4 concludes.

6

1 One shot make-or-buy choice

I consider a manufacturer who resells a unit of output that he obtains from a contractor or an

employee. In the absence of altruism, potential contractors, employees and the manufacturer

care only about what I call their material payoffs, which depend on their own income and

effort. The key difference between workers and contractors is that the manufacturer can give

orders to the former which, when followed, increase the value of output.

As discussed above, this fits with the legal definition of the employment relation. One

reason for this asymmetry could be that, as in Wernerfelt (1997), compensation cannot

be readjusted when these instructions are issued. Given that the contractor is entitled

not to follow these instructions, he might choose not to do so if these are given after his

compensation is set. Another reason could be that the manufacturer obtains the information

that is needed to issue these productive orders only if his agent is an employee. This, in

turn, could be due to two reasons. The first is that there is a complementarity between the

actions which ensure that orders are obeyed and the acquisition of information about which

orders would be useful. For example, both of these activities might benefit from having

the employee work in close proximity of his supervisor. Second, manufacturers are more

likely to own the assets used by employees than those used by contractor. This naturally

leads manufacturers to take a closer interest in the way the employees uses these assets and

provides an additional incentive for the employer to seek information about how these assets

ought to be used.

The timing of decisions is the following. First, the manufacturer decides whether to

be integrated or not. This decision is costless and determines whether the manufacturer

employs a single worker or a single contractor. If he chooses integration, the manufacturer

identifies a single worker drawn from a pool of identical workers while, otherwise, he identifies

a single contractor. Second, the worker or contractor that have thus been identified decide

whether to become altruistic. Third, there is a bargaining stage in which the manufacturer

signs a contract with either the worker or contractor. These contracts are required to be

7

be extremely simple. In the employment contract, the firm pays a wage pw in exchange for

having the worker follow the manufacturer’s instructions for one period. To simplify, the

worker can produce a single unit in this time period. In the case of an outside contractor,

the contract can only specify the price pc that the manufacturer pays on delivery of one unit.

I suppose that the pw and pc are determined by Nash bargaining between the agent and the

manufacturer where failure to reach agreement leads the agent to earn his reservation value

and allows the manufacturer to hire an outside agent by paying him the amount that leaves

him indifferent between working for the firm and remaining independent of the firm. After

these contracts are signed, the worker or contractor produce output which, at the end, the

manufacturer sells at a price z that depends on the good’s quality. Contracts between the

firm and either the worker or the contractor cannot depend on z.

This price equals z0 if workers or contractors incur the level of effort that they prefer,

namely e0. I suppose that both workers and contractors have a reservation value of r for

this effort. One reason workers may increase their effort is that employees must obey certain

orders issued by the employer.6 This is captured by supposing that, in the employment

relation, there is a probability φ1 that the manufacturer discovers a way of producing output

with a value of z1 rather than z0. For this increase in value to materialize, the worker must

exert effort e1, which costs him δ1 more than effort e0. The firm is entitled to require this

effort of its employee and, indeed, the firm cannot waive this right. Following Simon (1951)

there is no renegotiation with respect to the effort δ1. In the case where z1 − z0 > δ1 this

has limited effect on the equilibrium allocation since the employee would still make effort e1

if this renegotiation were allowed. Note that, for the purpose at hand it is not important

why buyers cannot obtain a good of value z1 from contractors, though one possible reason

for this is that the act of supervising workers allows the buyer to learn this.

There is also a second way in which either the employee or the contractor can raise the

6A simple, and somewhat realistic, formal model that yields this limited obedience consists of allowingthe employer to garnish his employee’s salary for one period if this employee fails to follow his instructions.More realistically, employees who fail to follow instructions are fired and, because this imposes a cost on theworker, outside agents (including co-workers, unions and the courts) help determine whether the cause forthis firing is “reasonable”.

8

value of output. By incurring effort e2 which costs the equivalent of δ2 units of income, the

worker or contractor have a probability φ2 to find a method to raise the value of output to

z2. This effort is made at the discretion of the worker or contractor, it cannot be compelled

even by the employer. If this effort yields a valuable idea, the value of output rises if the

idea is implemented. To simplify the analysis, suppose that this implementation requires no

additional effort and that the method that raises output to z2 still has social value when the

firm can increase output to z1, so that

z2 > z1 − δ1. (1)

Because the wage does not depend on whether e1 is carried out, the manufacturer prefers

z1 to z2 even if (1) is satisfied as long as z1 > z2. Choosing z1 is socially inefficient in this

case, however. While this set of parameters is of some interest, I focus on situations where

the firm implements z2 when it is available.

Given (1), the effort e2 is efficient as long as

φ2(z2 − z0 − φ1(z1 − z0 − δ1)) > δ2. (2)

In this one period case, the wage (or price to the contractor) is independent of the good’s

quality. The result is that, since e2 cannot be compelled and is costly to the agents, z2

cannot be obtained when the agents are selfish. Moreover

Proposition 1. If agents are selfish, the firm integrates if

z1 − z0 ≥ δ1 (3)

and remains non-integrated otherwise

Proof. Consider first the selfish contractor. Nash bargaining between this contractor

and the firm implies that the contractor earns his reservation wage r and the manufacturer

receives a good of value z0. The reason is that the contractor can earn r by not working for

the firm and the firm can obtain z0 − r by using an alternate selfish contractor.

9

Consider now a selfish worker. Whether the firm keeps the original worker or not, z1 > z0

implies that there is a probability φ1 that the firm obtains a good with value z1. Assuming

Nash bargaining over the wage before the firm forces the worker to exert effort of e1, the wage

offered to the inside worker is his reservation wage, namely r + φ1δ1. The worker accepts no

less because he knows the firm will insist on an effort of e1 and he gets no more because the

firm can obtain this outcome from any of the other available workers. This means that, the

firm is better off integrating if (3) holds. Q.E.D.

Note that integration leads to more valuable output for the firm ex post as long as

z1 > z0, which is weaker than (3). However, as in Simon (1951), the lack of recontracting

after the firm finds out a method for raising the value of output implies that, when (3) is

violated, the firm must pay the worker such a high wage ex ante that it is better off remaining

non-integrated.

I now show that endogenous altruism can lead the firm to use an outside contractor

even if (3) holds. My model of endogenous altruism is the following. A single agent (be it

an employee in the integrated case or a contractor in the non-integrated one) can become

altruistic towards the manufacturer by incurring a disutility which costs him the equivalent

of g units of income. This cost need not be interpreted as a cost of becoming altruistic

but, rather, can be a cost of providing credible proof of one’s altruism by, for example,

an appropriate choice of gifts (see Camerer 1988) . Alternatively, a side effect of becoming

altruistic is that one spends time with the object of one’s altruism (either because one enjoys

it or, again, as a way of demonstrating one’s altruism) and the cost is then the opportunity

cost of the alternative uses of this time.7

Becoming altruistic is beneficial in my model only if this altruism is observable. While

the observability of sentiments has been suggested before (see Homans 1950 p. 39) there is

no direct evidence for the observability of altruism or empathy. On the other hand, there

is evidence about a related sentiment, namely affect or “liking”. There have been many

7Another opportunity cost of altruism can arise if the agent has a limited capacity to help different people.In this case, an individual who becomes altruistic towards many people may start feeling a great deal ofguilt.

10

studies where people who know each other are asked whether they like one another. In

some of these studies, they have also been asked their opinion about the extent to which

they believe that others like them. In a study of college roommates Levesque (1997) asked

both these questions on a seven point scale.8 His subjects did not differ appreciably in

the average affect they reported for others not in the average perception of others’ affect

for them. There was considerable variance, however, in the extent to which any particular

subject liked different individuals and the extent to which any individual expected to be

liked by different roommates. At the same time, the correlation between the liking of a for

b and the extent to which b perceived that a liked him (or her) was an impressive .85. Thus,

these roommates perceived liking by others very accurately.9

I thus suppose that, once the agent has incurred the cost g, his altruism becomes apparent

to the manufacturer. Moreover, an altruistic agent no longer chooses his actions to maximize

his own material payoffs. Instead, his actions maximize a utility function that equals the

sum of his own material payoffs and λ times the material payoffs of the manufacturer. For

example, when the contractor faces choices concerning his level of effort, the part of the

manufacturer’s payoff that depends on this effort is simply given by z. Thus, the altruistic

contractor exerts effort e2 instead of e0 if

λφ2(z2 − z0) ≥ δ2. (4)

If the agent becomes altruistic, he must do so before he signs any contract with the

manufacturer. This captures the idea that becoming altruistic takes time while also ensuring

that the manufacturer cannot buy an agent’s altruism. After the agent becomes altruistic,

however, the manufacturer prefers to hire the altruistic agent over hiring alternate agents.

At this stage, the manufacturer and the altruistic agent negotiate over pc or pw. If the

manufacturer fails to reach agreement he gets to negotiate with a selfish agent where this

8Levesque (1997) also provides references for a few previous studies that looked at similar questions.9The perception of being liked may also have had an effect on people. While the extent to which a liked

b had a correlation of .82 with the extent to which b liked a (so that liking was reciprocated), the correlationof the extent to which a liked b with a’s perception of b’s liking for a was an even bigger .91. Thus theperception of being liked appears to be a trigger for liking others.

11

agent is a worker if the manufacturer is integrated and is a contractor otherwise.

I suppose that pc and pw are determined by Nash bargaining over material payoffs. In

the non-integrated case this means that the transfer from the manufacturer to the contractor

maximizes the product of the two material payoffs net of what they can obtain outside of the

relationship.10 Since outsiders are not altruistic towards the manufacturer, this means that

the expected gains from altruism are shared equally by the two parties. If the manufacturer

reaches agreement with the altruistic contractor, the manufacturer earns z0 +φ2(z2−z0)−pc

where pc is what this contractor receives while the manufacturer earns z0−r if no agreement

is reached. Similarly, the contractor earns pc − δ2 if he reaches an agreement and earns r

otherwise. Thus, Nash bargaining leads to a value of pc equal to

pc = r +φ2(z2 − z0) + δ2

2.

Now consider the stage where the manufacturer must decide whether to become altruistic

or not. I suppose this decision maximizes the contractor’s material payoffs. As discussed

in Rotemberg (1994), a variety of reasons can be given for this assumption. The simplest

is that altruism is chosen by a “rational self” which maximizes material payoffs and uses

altruism as a commitment device.

If (4) holds, the altruistic contractor’s material payoffs are are pc−δ2 so that the contractor

benefits by spending g and becoming altruistic if

φ2(z2 − z0)− δ2

2− g > 0. (5)

With this altruism, the manufacturer’s profits, πc, are z0 + φ2(z2 − z0)− pc or

πc = z0 − r +φ2(z2 − z0)− δ2

2. (6)

Now consider the integrated firm. Since the firm implements the worker’s method when

it leads to z2, a worker who exerts effort e2 reduces the probability that he will have to exert

10Similar results can be obtained by letting the transfer maximize the product of the “psychologicalpayoffs,” which include the vicarious enjoyment of the manufacturer’s utility by the contractor. The analysisis more complex, however.

12

effort e1 from φ1 to φ1(1− φ2). A worker who becomes altruistic thus exerts effort e2 if

λφ2[z2 − z0 − φ1(z1 − z0)] ≥ δ2 − φ2φ1δ1. (7)

Both this condition and the corresponding condition for contractors (4) require that λ be

greater than some threshold. If δ1 is zero, (7) requires a higher λ because the more muted

effect of e2 on profits under integration implies that workers get less vicarious utility from

e2. On the other hand, increases in δ1 reduce the degree of worker altruism required to carry

out e2 because workers are less likely to be asked to do e1 if e2 succeeds.

Supposing an integrated firm reaches agreement with an altruistic worker and (7) holds,

the firm earns φ2z2 + (1− φ2)(z0 + φ1(z1 − z0))− pw. If it fails to reach this agreement, the

firm earns z0 + φ1(z1 − z0 − δ1)− r. The worker’s material payoff is pw − δ2 − φ1(1− φ2)δ1

if he reaches agreement while he again earns r if he earns his reservation wage elsewhere.

With Nash bargaining, pw ensures that the expected increases in material payoffs are divided

evenly so that

pw = r + φ1δ1 +φ2[(z2 − z0)− φ1(z1 − z0)] + δ2 − φ1φ2δ1

2

and profits with an altruistic worker are

πw = z0 − r + φ1(z1 − z0 − δ1) +φ2[z2 − z0 − φ1(z1 − z0)]− δ2 + φ1φ2δ1

2.

Using the formula for πc in (6), this becomes

πw = πc + φ1

(1− φ2

2

)z1 − z0 − δ1

2. (8)

The worker benefits from becoming altruistic if pw− r− δ2−φ1(1−φ2)δ1 exceeds g or if

φ2(z2 − z0)− δ2 − φ1φ2(z1 − z0 − δ1) > 2g. (9)

If z1 − z0 > δ1, condition (9) is more stringent than condition (5). The left hand sides of

these conditions are, respectively, the amounts that worker and contractor receive for their

13

altruism. These differ because the firm pays less for worker altruism as a result of its access

to e1.11

This difference in the private rewards to altruism lead to the first set of sufficient condi-

tions for the firm to prefer to be non-integrated even when (3) holds so that the manufacturer

would integrate both in the absence of altruism and if he could simply buy an agent’s altruism

by paying him g. This is

Proposition 2. If (4) holds while, at the same time

1− φ2

2<

2g

φ2(z2 − z0)− δ2

< 1, (10)

there exists a strictly positive range of values for φ1(z1 − z0 − δ1), namely

φ2(z2 − z0)− δ2 − 2g

φ2

< φ1(z1 − z0 − δ1) <φ2(z2 − z0)− δ2

2(11)

such that the manufacturer prefers to be non-integrated.

Proof. Multiplying the first two expressions in (10) by 2[φ2(z2− z0)− δ2] and rearranging,

one obtains

2[φ2(z2 − z0)− δ2 − 2g] < φ2[φ2(z2 − z0)− δ2],

which establishes that values for φ1(z1 − z0 − δ1) exist in the range given by (11).

The rest of the proof proceeds by assuming that (7) holds so that an altruistic worker

does indeed carry out effort e2. However, if this condition is violated profits under integration

are even lower than I suppose, and the worker gains even less by becoming altruistic. Thus,

the proof extends readily to the case where (7) is violated.

The first inequality in (11) implies that (9) is violated so the worker does not choose to

become altruistic (again even if (7) holds). Given that (4) holds, the second inequality in (10)

ensures the contractor becomes altruistic. Thus the manufacturer faces the choice between

11This may seem somewhat reminiscent of Grossman and Hart (1988) if one looks at the acquisition ofaltruism as a type of specific investment that is made before compensation is set. One could then say thatthe contractor receives a higher return on his investment than the worker because the firm does not haveaccess to e1 in the non-integrated case. Note, however, that unlike an essential attribute in the Grossmanand Hart (1988) model, ownership of one particular piece of capital is not sufficient to give access to a goodof quality z1. Rather, this option arises only if the buyer also gets to direct the actions of the supplier.

14

an altruistic contractor, which yields the manufacturer πc and a selfish worker, which yields

the firm z0 + φ1(z1 − z0 − δ1). The second inequality in (11) ensures the firm prefers the

former. Q.E.D.

What is needed for this outcome is that both g and φ1(z1 − z0 − δ1) fall in intermediate

regions. The surplus from the effort e1 must be large enough that it reduces sufficiently the

social value of the worker’s altruism while it must be small enough that the firm does not

prefer a selfish worker to an altruistic contractor. When this surplus is in this range, the

cost of altruism g can be small enough that the contractor wishes to become altruistic while

being large enough that the worker does not.

The fact that altruism can be less effective at inducing the effort of workers gives rise to

a second set of sufficient conditions for non-integration to be optimal even when (3) holds.

This is given by the following proposition.

Proposition 3. Ifδ1

z1 − z0

<δ2

φ2(z2 − z0)(12)

there exists a positive range of values for λ such that 0 ≤ λ ≤ 1 and

δ2

φ2(z2 − z0)< λ <

δ2 − φ1φ2δ1

φ2(z2 − z0 − φ1(z1 − z0)). (13)

For λ in this range, the contractor is willing to exert effort e2 while the worker is not (with

lower values of λ neither does so.) Moreover, for this range of λ, if (5) holds while

φ1(z1 − z0 − δ1) <φ2(z2 − z0)− δ2

2, (14)

the manufacturer prefers to be non-integrated.

Proof. Inequality (12) implies that

−δ2(z1 − z0) < −δ1φ2(z2 − z0).

Multiplying both sides by φ1φ2, adding δ2φ2(z2 − z0) to both sides and rearranging yields

δ2φ2[z2 − z0 − φ1(z1 − z0)] < φ2(z2 − z0)[δ2 − δ1φ1φ2].

15

This implies that positive values of λ can be found that satisfy (13). At the same time,

(2) implies that the left hand side of (13) is smaller than 1 so this inequality is also consistent

with λ ≤ 1.

The first inequality in (13) ensures that (4) holds so that, since (5) holds as well, the

contractor becomes altruistic and makes the effort e2. The second inequality in (13) implies

that, instead, (7) fails to hold so that workers do not make the effort e2 even if they become

altruistic. This means that workers remain selfish and the firm confronts once again the

choice between a selfish worker and an altruistic contractor. The inequality in (14), which is

the same as the second inequality in (11), ensures that the manufacturer prefers the former.

Q.E.D.

The inequalities in (13) ensure that the altruism parameter λ is sufficient to induce

cooperation by contractors but not sufficient to ensure it on the part of workers. There is,

in a sense, a tension between (14) and (12). The former requires that the net benefits of e2

be large relative to those of e1 while the latter requires that the ratio of benefits to costs be

larger in the case of e1 than in the case of e2. In other words, the benefits of e1 must be

small enough that the firm prefers an altruistic contractor who makes the effort e2 but the

benefits of e1 must also be large enough that they reduce sufficiently the worker’s vicarious

enjoyment from making effort e2. Because (12) involves ratios, it can be satisfied with low

net benefits for e1 as long as the cost δ1 is low. If δ1 is zero, for example, one can find values

of λ that satisfy (13) for any positive value of z1 − z0.

A simple interpretation of Proposition 3 is that, if (12) holds, the minimum altruism

that leads the contractor to seek the innovation that raises the value of output to z2 is lower

than the minimum altruism that achieves this for a worker. The reason, again, is that the

contractor expects to increase the buyer’s material payoffs by more when he makes the effort

e2. This means that, if the expenditure of g leads only to a small degree of altruism, the

buyer can only expect the contractor to become usefully altruistic.

Formally, this model of altruism is a model of investment. This raises the obvious question

of whether identical results could be obtained using a model of investment in physical goods.

16

What would be required, however, is that this investment actually eliminate the ex post cost

of providing a good with quality z2. Any costs of increased quality would have to be incurred

before the buyer and the seller agree to transact at the price pc or pw.

The essential feature of the model, then, is that altruism from seller to buyer is observed

only in situations where there are such ex post opportunities to improve quality at a cost.

The model then has more specific empirical implications in the plausible case where the

maximum altruism λ is relatively low and where the cost of carrying out effort e1 rather

than e0 is negligible (because the worker is simply doing “his job” in either case.) It then

follows that altruism from seller to buyer is observed only when the firm uses an independent

contractor and that such contractors are used only if the seller’s ex post ideas for product

improvement are valuable relative to the buyer’s ideas.

2 Repeated Purchases in an Unchanging Environment

I now turn to a setting where altruism is not essential for ensuring that high quality goods are

produced. Purchases are repeated and, as in Shapiro and Stiglitz (1984) and Baker, Gibbons

and Murphy (2001) the purchaser can stop his relationship with the seller in response to poor

performance.12 One reason to study this settings is to understand whether altruism still plays

a role at all. This is important because, in practice, altruism tends to arise in settings where

interactions are indeed repeated. The second, and related reason is that period-by-period

Nash bargaining is not attractive as a mechanism for setting compensation in a repeated

setting, and it seems worthwhile to understand whether the earlier results are sensitive to

setting compensation in this way. Lastly, the analysis of repeated purchases provides a

12This approach is also similar to that in the classic article by Klein and Leffler (1981). The main differencewith Klein and Leffler (1981) is that they suppose that the delivery of low-quality goods to one customer affectthe purchases of others as well. This assumption is very appealing for mass-produced branded products,which are the focus of Klein and Leffler (1981) analysis, since modern manufacturing techniques seek toensure that the quality of these products is uniform. In the case of customized products or services, however,the connection between the quality provided to different customers in less tight. It is even possible that theprovision of low quality to one customer frees up the supplier’s time so he has more time to provide highquality for others. Thus the quality provided to one customer conveys little information to others. This fitswith Uzzi (1997) who reports that many suppliers have “special” relationships with some customers whilethey have “arm’s length” relations with others.

17

foundation for the later study of buyer altruism in the presence of demand fluctuations.

Suppose the manufacturer buys one unit per period. The discount factor is β and the

manufacturer offers a price pc to the contractor, or pw to the worker, at the beginning of

each period. If the contractor accepts, he receives pc upon delivery of one unit. Similarly, if

the worker accepts, he is paid pw if he works that period.

I consider the following strategy for a manufacturer. If he offers a price that exceeds

either r (in the case of a contractor) or r + φ1δ1 (in the case of a worker), he continues to

offer the same price to the same supplier until something occurs that leads the manufacturer

to end to the relationship. If the manufacturer ever deviates and lowers his price, he then

keeps the price lower from that point onwards. In the case of the worker or contractor, I

consider the strategy of making effort e2 in every period in which he is offered pc (or pw) and

reducing this effort to e0 immediately after the manufacturer offers a lower price.

One important determinant of the equilibrium outcome is the trigger that leads the man-

ufacturer to stop his relationship. Because the cessation of purchases is a drastic punishment

and because output can commonly be worth z0 also when the agent exerts high effort, it does

not make sense to punish the agent every time a good worth z0 is delivered. An alternative,

following Radner (1985) would be to let the manufacturer follow a “review strategy” where

he periodically looks at the total value of output since the last review and fires the agent

only if this total value falls short of a“trigger” level.

I consider a simpler alternative, in which the manufacturer has bounded recall so he only

remembers the value of output in the previous period (though he does remember forever

whether he has fired a particular agent). At the same time, the manufacturer has access to

a crude monitoring technology. Whenever the value of output is z0, there is a probability

ρc that the manufacturer observes whether the contractor has made effort e0 or e2 and a

probability ρw that he makes the corresponding observation in the case of a worker. If

the manufacturer observes that the contractor has made effort e0, he stops buying with

probability θc. In the case of a worker, the corresponding probability that he is fired is θw.

Lastly, I let ξi, where i equals either c or w, be equal to θiρi. Thus ξi is the probability that

18

the relationship with an agent that makes effort e0 is severed.

Two simple cases deserve to be considered. The first, which is consistent with Baker,

Gibbons and Murphy (2001), is to suppose that ρc = ρw while θc = θw = 1. Thus the

quality of the observations is the same in the integrated and the non-integrated case and

the relationship is severed whenever it is observed the agent made effort e0. I also consider

the alternative explored in Rotemberg (1991) where θc is equal to one while ξw is equal

to zero. This captures, in extreme form, the idea that severing relationships with outside

suppliers is easier in principle than is severing relationships with employees. As discussed in

the introduction, this difference is partly due to the law.

The cost of firing contractors may also be lower as a direct consequence of the firm’s

ability to give orders to its employee. This ability implies that, even after an employer

ascertains that the employee has carried out effort e0 and not effort e2, the employer may

prefer not to sever the relationship if the employee is good at carrying out effort e1.13 In

other words, the existence of another range of activities may imply that it is not credible

for the firm to fire an employee who carries out effort e0 instead of e2. This in no way

requires the irrelevance of the analysis of Shapiro and Stiglitz (1984), it simply requires that

the events that trigger the firing of employees be different (and presumably more egregious)

than those that trigger the severing of relationships with outside suppliers. The firm may,

for example be happy to fire employees who do not carry out effort e1 but may be reluctant

to let go those employees who prove adept at following these instructions.

I start by studying a contractor with altruism parameter λ. To avoid the implication

that someone who becomes altruistic sees an instantaneous effect on the level of his utility

through his vicarious enjoyment of another’s consumption, suppose that an altruist gains

utility only when his own actions raise the utility of the object of his altruism. Thus, a

contractor whose altruism equals λ gains λ(z2 − z0) when the manufacturer receives a good

worth z2. This means that, in each period where he makes effort e2, his total payoff is

13A complete model of this would presumably require some heterogeneity in the quality of matches betweenemployees and employers so that e1 does not have the same effect with all these matches.

19

pc − δ2 + λφ2(z2 − z0).

If he continuously provides high effort, he is never fired and can expect to earn this

payoff in every period. A contractor that deviates and makes effort e0 for a single period

obtains a material payoff of pc in the period of the deviation and has a probability ξc of

receiving his reservation wage r per period in subsequent periods. With probability (1− ξc),

his subsequent per-period payoff returns to pc − δ2 + λφ2(z2 − z0) (because I am studying a

one period deviation). Thus this deviation is not profitable as long as

(1− β)pc + β[ξcr + (1− ξc)(pc − δ2 + λφ2(z2 − z0))

]≤ pc − δ2 + λφ2(z2 − z0)

or

pc ≥ r +

[1 +

1− β

βξc

] (δ2 − λφ2(z2 − z0)

). (15)

As long as β is strictly smaller than one, the minimum price that prevents this deviation

exceeds the cost of providing effort e2 if the employee is selfish and λ = 0. Higher values of

λ lower this minimum price and the same is true for higher values of ξc, since these imply

that a deviation is more likely to be punished. Condition (15) is also sufficient for deterring

deviations that last a finite number of periods since it deters such deviations in the last of

these periods. Lastly, the existence of discounting implies that the contractor has nothing

to gain from deviating infinitely into the future.

Consider deviations by the manufacturer from the proposed equilibrium. If the manu-

facturer offers any price between r and the minimum price that satisfies (15), the contractor

expects this low price to prevail from then on and he therefore makes an effort equal to e0.

This means that the manufacturer who deviates has nothing to gain from paying more than

r. Paying pc in the expectation of inducing effort e2 is preferable to this deviation if

z0 + φ2(z2 − z0)− pc ≥ z0 − r

or

pc ≤ r + φ2(z2 − z0). (16)

20

When a contractor is paid the minimum price that satisfies (15), this condition can be written

as

(1− β + βξ)δ2 − βξcφ2(z2 − z0) ≤ (1− β + βξc)λφ2(z2 − z0). (17)

When the contractor is selfish so λ = 0, this conditions requires that the social benefits

from making the effort e2, φ2(z2− z0)− δ2 be somewhat larger than zero. A higher λ lowers

the minimum price that deters deviations by the contractor and thereby makes it easier to

satisfy (16). So, when the left hand side of (17) is positive, this inequality puts a minimum

bound on λ.

Manufacturer profits when (17) is satisfied are

πc = z0 − r + φ2(z2 − z0)

[1 + λ

(1 +

1− β

βξc

)]− δ2

(1 +

1− β

βξc

). (18)

Because profits rise with λ, altruism tends to arise in equilibrium. To see this, suppose

that before the repeated interaction starts, there is a phase of the game where potential

suppliers can raise their altruism parameter from λ = 0 to λ = λ > 0 at cost g. Suppose

again that there is a large pool of potential contractors and let them choose sequentially

whether to spend g or not. After each has made his choice, the manufacturer picks a

contractor with whom he interacts until the relationship ends. The manufacturer obviously

picks an altruistic contractor, if one is available. The analysis is simplified by supposing

that, if none is available, he picks the last contractor who had a chance to become altruistic

while, if several are altruistic, he picks the first contractor who spent g to raise his λ to λ.14

If the first contractor becomes altruistic, the present value of his material benefits is

pc−δ2−r1−β

− g. If the manufacturer is rational, he sets pc to the minimum value such that (15)

holds. Thus, the present value of the contractor’s material benefits is positive if

[1 +

1− β

βξ

] (δ2 − λφ2(z2 − z0)

)− δ2 ≥ (1− β)g. (19)

14These specific assumptions ensure that some contractors know that they will not be picked if they donot become altruistic. With a sufficiently large number of potential contractors, it must be the case thatmost contractors have a small probability of being picked even if all contractors remain selfish. The analysisis then insensitive to the particular way the manufacturer picks contractors when they are all selfish.

21

The left hand side captures the per period rents earned by the contractor. These are

positive when λ = 0 and falling in λ. Thus, for λ and g small enough, (19) is satisfied.

Whenever this expression is satisfied, altruism emerges in equilibrium. The first contractor

who has a chance to become altruistic does so because this means his rents are positive

rather than zero. If, instead, (19) is violated, no contractor becomes altruistic because doing

so leads to losses.

Now consider the analogous analysis for the case of a worker. To focus on the effect

of the firm’s ability to give orders to its employees, the rest of the model is the same. In

particular, suppose somewhat counterfactually that there is an initial period where workers

choose their altruism and the firm then chooses which worker to hire. Before looking at

the decision of whether to become altruistic, however, consider the incentive of a worker to

deviate from making the effort e2 for one period. As before, the manufacturer’s strategy is

to pay pw except that, when the employee makes an effort e0, the manufacturer severs the

relationship with probability ξw.

An employee who deviates for one period and makes an effort e0 gets an expected material

payoff of pw − φ1δ1 in that period and has a probability ξw of receiving r from that point

onwards. With probability (1− ξw) the employee gets the same amount after the deviation

as he would in each period in which he does not deviate. This amount equals

pw − δ2 − (1− φ2)φ1δ1 + λφ2(z2 − z0 − φ1(z1 − z0)). (20)

Thus, deviations are deterred if

pw ≥ r + φ1δ1 +

[1 +

1− β

βξw

] (δ2 − φ1φ2δ1 − λφ2(z2 − z0 − φ1(z1 − z0))

), (21)

Once again, the minimum price that deters deviations falls when either λ or ξw rise.

An important consequence of (21) is that, while increases in λ reduce the lowest value of

pw that satisfies (21), they do so by less than they reduce the lowest value of pc that satisfies

(15). The reason is that altruism has a smaller effect on the willingness of the employee to

find ways of raising output to z2 than it does on the willingness of a contractor to do so. This

occurs, in turn, because raising output to z2 is less valuable for integrated manufacturers.

22

The profits of a manufacturer whose employee exerts effort e2 while being paid pw are

πw = z0 + φ1(1− φ2)(z1 − z0) + φ2(z2 − z0)− pw.

With the minimum pw that satisfies (21), these profits become

πw = z0 − r + φ1(z1 − z0 − δ1)− (δ2 − φ1φ2δ1)

(1 +

1− β

βξw

)

+φ2(z2 − z0 − φ1(z1 − z0))

[1 + λ

(1 +

1− β

βξw

)](22)

Alternatively, the manufacturer could pay r +φ1δ and let the employee exert effort equal

to either e0 or e1 depending on whether the manufacturer finds a way to raise output to z1.

This yields profits of z0 − r + φ1(z1 − z0 − δ1) so that paying pw for effort e2 is preferable if

φ2(z2 − z0 − φ1(z1 − z0)) ≥(

1 +1− β

βξw

) (δ2 − φ1φ2δ1 + λ(z2 − z0 − φ1(z1 − z0))

). (23)

Consider first the case where ξw is small. This captures the idea that, while workers

can be fired for poor performance, the performance has to be significantly poorer than for

an outside supplier providing the same service. As discussed above, this can be due to laws

protecting workers from dismissal.15 It can also be due to the advantages of keeping a worker

that is good at carrying out the activities I have grouped under e1.

In either case, the effect of a sufficiently low value of ξw is to ensure that (23) is violated

regardless of λ so that the manufacturer prefers to pay r + φ1δ1 to obtain a good with

an expected value of z0 + φ1(z1 − z0). This means that, in equilibrium, workers must be

selfish. Combined with the earlier analysis for contractors, this model thus rationalizes the

appearance of higher levels of altruism among parties participating in inter-firm transactions.

For the rest of this section, suppose that ξc = ξw. While arguably less realistic, this

symmetric benchmark is of some interest, particularly because altruism can increase the

benefits of vertical separation even in this case. Comparison of (18) and (22) establishes

immediately that

15This raises the question of why workers are more protected from firing by laws. One reason could bethat a worker who loses his job may incur a larger loss in standard of living than a contractor who loses anequivalent contract because contractors have better access to alternative opportunities. This, in turn, maybe a side effect of the employer’s control over the employee.

23

Proposition 4. If ξw = ξc and λ = 0 while (17) and (23) both hold, then

z1 − z0 > δ1

(1− φ2(1− β)

(1− φ2)βξ

)(24)

is sufficient for integration to be optimal.

Proof. Since (17) and (23) both hold, both the contractor and the employee would exert

effort e2. The proposition then follows from comparing (18) to (22) Q.E.D..

More generally,

Proposition 5. If ξw = ξc and λ = 0, (3) implies that the manufacturer hires a worker.

Proof. If both (17) and (23) hold, this follows from Proposition 4. If (23) fails to hold,

profits with a worker are higher than the expression in (22). As a result, (24) also implies

that profits with integration exceed those with an independent contractor when (23) fails

and (17) holds. If they both fail, neither type of agent makes the effort e2 so the one-shot

outcome is repeated from period to period and (3) is sufficient for the manufacturer to hire

a worker. Lastly, if (17) fails and (23) holds, the contractor would yield profits of zo − r per

period to the manufacturer and, given (3), (23) implies that profits with a worker making

the effort e2 are higher. Q.E.D.

This proposition shows that, when the agents are selfish and the ξ’s are equal, repetition

of the interaction does not make the manufacturer prefer an outside contractor. Indeed, the

opposite is closer to true. Since (24) is strictly weaker than (3), it is possible for the firm

to prefer to integrate even though contractors would be preferred to workers in a one-shot

interaction. A benefit of integration when interactions are repeated is that workers receive

fewer rents when carrying out effort e2 because one motivation for carrying out this effort is

to avoid having to make effort e1.16

16This result is consistent with the insight of Baker, Gibbons and Murphy (2001) that a firm’s choicebetween integration and non-integration remains non-trivial even with repeated interactions. However, whilethe difference between integration and non-integration in similar in the two analyses, it is not identical. Baker,Gibbons and Murphy (2001) focus on the exclusive ability of the contractor to take actions that raise hisrewards outside the relationship while I focus on the firm’s exclusive ability to control its employees. In bothmodels, the worker is assumed to be more constrained than the contractor but my analysis applies also incases where the price paid to the contractor is independent of the actions the contractor takes outside therelationship.

24

Endogenous altruism, on the other hand, can lead the manufacturer to use an outside

contractor even when (3) holds . In particular,

Proposition 6. If (3) holds while ξc = ξw = ξ and

φ2(1− β + βξ)λ > βξφ1z1 − z0 − δ1

z2 − z0

−[βξφ2 − (1− β + βξ)

δ2

z2 − z0

](25)

and

βξ(1− φ2) + [φ2(1− β)− βξ(1− φ2)]δ1

z1 − z0

< φ2(1− β + βξ)λ < (1− β)δ2 − βξg

z2 − z0

(26)

the firm is better off with a contractor.

Proof. Condition (25) is equivalent to requiring that the expression in (18) with λ = λ

exceeds the profits with a selfish worker z0 − r + φ1(z1 − z0 − δ1). Given that (3) holds, this

ensures that profits with an altruistic contractor also exceed profits with a selfish contractor

who is paid r.

Using (22) and (18), the difference between the profits with integration and profits with-

out are

φ1(1− φ2)(z1 − z0)− φ1δ1 + φ1φ2[δ1 − λ(z1 − z0)]

[1 +

1− β

βξ

]

The first inequality of (26) ensures this is negative for λ = λ. This means that profits

are higher with an altruistic contractor than with a worker with the same level of altru-

ism. Lastly, the second inequality in (26) is simply a restatement of (19); it ensures that

contractors are willing to acquire this level of altruism. Thus, when these conditions hold,

the contractor is willing to become altruistic and profits with an altruistic contractor exceed

profits with any other type of agent. Q.E.D.

As long as the benefits from e2 are sufficiently larger than the benefits from e1, condition

(25) holds. This condition simply ensures that e2 is sufficiently valuable that a repeated

relation that gives rise to e2 is better than simply giving orders to a worker. Condition

(26) is more subtle. It requires that λ be neither too large nor too small. If λ is too large,

contractors are unwilling to become altruistic because the resulting rents are insufficient. If

25

λ is too small, the tradeoff faced by the firm is too similar to that faced when λ = 0 and, in

this case, (3) is sufficient to ensure that the firm prefers effort e2 with a worker over effort

e2 with a contractor. However, because increases in λ reduce contractor rents more rapidly

than worker rents, intermediate values of λ do exist where the firm prefers a contractor.

3 Repeated Purchases with Fluctuations in Final De-

mand

In this section I neglect the employment relation to study conditions that lead not only

to contractor altruism but also to manufacturer altruism towards the contractor. One way

of rationalizing this analysis is by supposing that ξw is significantly smaller than ξc while

z1 − z0 − δ1 is small. Manufacturer altruism can emerge in this case if demand fluctuates so

that a selfish manufacturer does not always make purchases from an altruistic contractor.

The role of manufacturer altruism is then to increase the frequency of these purchases.

I capture the randomness in demand by supposing that the manufacturer receives sz for

his unit if he sells it, where s is independently distributed over time and drawn from a c.d.f.

F (s). Without loss of generality, I suppose that the support of this distribution is given by

[α, 1] where α ≥ 0. I also suppose that the manufacturer knows the current value of s when

he decides whether or not to order a unit from a contractor.

The setup I consider has the following structure. First, the contractors choose their

altruism parameter, as before. Then the manufacturer chooses one particular contractor. At

that moment, the manufacturer decides whether he wishes to become altruistic towards the

contractor. After this, in each period, the manufacturer can make offers to purchase goods

from either the altruistic contractor or from other contractors. After such an offer is made,

the contractor who accepts it determines his level of effort.

Except for the stage where the manufacturer chooses his altruism, this timing of decisions

is the same as in section 2. In the analysis of section 2, this additional stage would have had

no effect. The reason is that the agents were influenced only by the prices (pc and pw) they

could expect to earn in the future. While manufacturer altruism could have an effect on

26

these prices, that would not have increased manufacturer profits since I focused on equilibria

were the prices were such that profits were maximized.

The randomness of s implies that it is no longer reasonable to require that the manu-

facturer purchase one unit from the contractor in each period. If s is sufficiently low such

purchases are inefficient. I thus suppose that the manufacturer determines when he makes

purchases from contractors. I also focus only on equilibria where the price of such purchases

is independent of s. This independence of the price on the state of final demand could be

rationalized by supposing that contractors do not know the current value of s while they

also fail to remember the past prices they were offered by the manufacturer. They are able

to remember, however, whether they were ever offered a price so low that they chose not to

make the effort e2. This means that equilibria may exist where contractors make effort e2

when they are offered a price no smaller than a cutoff price p and where they cease making

this effort if they are ever offered a lower price.

Under these assumptions, a selfish manufacturer would offer p to a contractor that he

expected to make the effort e2 if and only if

sz0 + φ2(z2 − z0)s− p ≥ max(0, sz0 − r).

The left hand side of this expression are the profits from paying p for e2 while the right hand

side are the highest profits that the manufacture can earn if he does not pay p. These latter

profits equal sz0− r when it is worthwhile to hire a contractor who makes effort e0 and zero

otherwise.

Suppose that, instead of being selfish, the manufacturer feels altruism towards the con-

tractor. I capture this altruism by the parameter λm. The effect of this parameter is to lead

the manufacturer to maximize the sum of his own material payoffs and λm times the increase

in the material payoffs of the contractor that is due to the actions of the manufacturer. The

increase in the contractor’s material payoffs from being offered p assuming this leads to the

effort e2 equals p − δ2 − r. Thus, an offer of p to a contractor whom he expects to make

effort e2 is preferable for a manufacturer with altruism parameter λm than either making no

27

offer or making an offer of r to a contractor who will make effort e0 as long as

sz0 + φ2(z2 − z0)s + λm(p− δ2 − r)− p ≥ max(0, sz0 − r). (27)

This inequality can be interpreted in two ways. First, it gives the minimum s, which I

label s, such that the manufacturer is willing to offer p if he expects the contractor to make

effort e2. Additionally, (27) can be seen as defining a “maximum offer curve” which gives the

maximum p that a firm is willing to pay for a given s. Increases in s raise the maximum-offer

price as do increases in λm in those cases where p exceeds δ2 + r. This is shown graphically

in Figure 1 which depicts “maximum offer curves” for r = 0, φ2 = .6, (z2 − z0) = 15.5 and

δ2 = 6, though their qualitative properties do not depend on these parameters. The line

that starts from the origin corresponds to the case where λm equals zero while the other line

corresponds to λm = .2. The two lines cross at the point where φ2(z2 − z0)s = δ2 so that

effort e2 is socially optimal. For higher values of s, altruism on the part of the manufacturer

raises the price the manufacturer is willing to pay, or imply that a selfish manufacturer would

have ordered only if s were larger than the minimum s that leads the altruist to place an

order.

For s < s, the manufacturer’s offer depends on whether sz0 is greater than or smaller

than r. If it is greater, the manufacturer offers r to a contractor whom he expects to make

effort e0 and otherwise he simply refrains from buying the good. To simplify the analysis,

I suppose that r < αz0, so the manufacturer always buys a unit. Manufacturer profits are

then

πm =∫ 1

α[sz0 − r]dF (s) +

∫ 1

s[φ2(z2 − z0)s− p]dF (s). (28)

I now turn to analyzing the contractor and let λc denote his altruism parameter. The key

issue facing the contractor is whether he should exert effort e2 when he is offered p. As before,

I consider equilibria where, if the contractor fails to make this effort, there is a probability

ξ that the manufacturer learns this and ceases making offers of p to the contractor. The

contractor expects that if, instead, the manufacturer does not learn that the contractor has

exerted a low level of effort, he will offer p again whenever s is above the cutoff value s.

28

Let Ω be given by

Ω =∫ s

αrdF (s)+

∫ 1

s[p−δ2+λcφ2(z2−z0)s]dF (s) = r+

[1−F (s)

][p−r+λcφ2(z2−z0)E(s|s ≥ s)

].

This is the expected one-period benefit to the contractor of being ready to provide effort

e2 when receiving a price p. With probability F (s) this benefit equals only r because the

manufacturer fails to place an order with the contractor. The contractor then chooses not

to deviate from the equilibrium where he makes effort e2 when he is offered p as long as

p +β

1− β

(ξr + (1− ξ)Ω

)≤ p− δ2 + λcφ2(z2 − z0)E(s|s ≥ s) +

β

1− βΩ.

Rearranging and using the definition of Ω, this requires that

p− r ≥[δ2 − λcφ2(z2 − z0)E(s|s ≥ s)

] [1 +

1− β

βξ[1− F (s)]

]. (29)

Inequality (29) defines a “minimum requirement curve” which gives the minimum p such that

the contractor is willing to make effort e2. Leaving aside contractor altruism, an increase

in s reduces the frequency with which the manufacturer places orders and thus requires

that the contractor receive a higher price if he is to be restrained from deviating. His total

future rents must remain the same but, because he collects rents less frequently, they must

be higher in the periods that he collects them. As before, an increase in contractor altruism

lowers the price the contractor must be paid to induce him to provide high quality.

Figure 2 depicts “minimum requirement curves” for the same parameters as those in

Figure 1 and β = .99, ξ = .2, F uniform, α = .2 and two different values of λc. When

λc = 0, the slope of this line is proportional to f(s)/(1− F (s))2. If the hazard f/(1− F ) is

monotone, as I assume throughout, this slope is increasing in s. An increase in λc not only

lowers p when s takes the minimum value of α; it also lowers the slope of p with respect to

s for each value of s. The reason is that the conditional mean E(s|s ≥ s) is increasing in

s. Thus, increases in s raise the vicarious benefits of an altruist when he makes effort e2,

because they imply that the manufacturer is gaining more through this altruistic act.

An equilibrium with high quality for given levels of the two altruism parameters, if one

exists, is a pair of values for p and s such that p is the minimum price that satisfies both

29

(27) and (29) for s = s. The reason for selecting the minimum price, i.e, the price that

maximizes manufacturer profits, is that the manufacturer would never choose to make λm

greater than one and, once (29) and (27) are satisfied, increases in p are simply transfers from

the manufacturer to the contractor. The equilibrium price is on the “minimum requirement

curve” but it can be below the “maximum offer curve” for s = s.

As in the case of constant demand, there are cases where no p can ensure that a selfish

contractor produces high quality goods that are purchased by a selfish manufacturer. Two

sufficient conditions for this outcome are

δ2

[1 +

1− β

βξ

]> φ2(z2 − z0)α (30)

and

δ2f(α)1− β

βξ> φ2(z2 − z0). (31)

The first ensures that the “maximum offer curve” is below the “minimum requirement

curve” at s = s = α. This condition is actually necessary to rule out an equilibrium where

high quality is provided for all values of s. The second of these inequalities ensures that the

slope of the ”minimum requirement curve” is steeper at α than the slope of the “maximum

offer curve” so that, given the monotone hazard of f , the former curve lies everywhere above

the latter.

Whether the outcome without altruism involves the provision of high quality or not,

contractor altruism arises in equilibrium if the cost of this altruism is low enough. This is

shown in the following proposition.

Proposition 7. If both manufacturer and contractor find any level of altruism costless, the

equilibrium is the first best with s = max(α, δ2φ2(z2−z0)

) and p − r = δ2. This equilibrium

requires a strictly positive value for λc but the equilibrium is consistent with λm = 0.

Proof. That this pair of s and p induces the first best outcome is immediate since the social

value of effort e2 is φ2(z2−z0) and the social cost is δ2. That this pair is consistent with (27)

when setting λm = 0 is immediate as well. It is also obviously consistent with (29) for some

30

strictly positive value of λc. Contractors have no reason to deviate from this λc because their

total rents at this equilibrium are zero since they are being paid the cost of their effort. By

the same token, λc cannot be smaller than this value because contractors would earn rents

otherwise. Lastly, manufacturers have no reason to acquire positive altruism. Raising λm

from zero neither changes p nor s. The latter is not affected because for s below δ2φ2(z2−z0)

,

increases in λm actually lower the maximum offer price. Q.E.D.

The role of contractor altruism is the same as in the previous section; it lowers contractor

rents and facilitates the production of high quality goods. With sufficient contractor altruism,

the inefficiencies due to the lack of observability of effort disappear so manufacturer altruism

plays no role. Manufacturer altruism can play a role, however, when contractor altruism is

costly. To show this, I focus on the case where varying λm costs no resources while contractor

altruism is exogenously set to λ. Implicitly, the cost g of this altruism is assumed to be lower

than the rents collected by the contractor while higher levels of altruism are assumed to be

prohibitively expensive.

With this exogenous λc, I provide two sets of sufficient conditions for λm > 0 in equilib-

rium. The first applies to the case where, without manufacturer altruism, contractor effort

is always e0

Proposition 8. Suppose that

p ≡[δ2 − λφ2(z2 − z0)E(s)

] [1 +

1− β

βξ

]> φ2(z2 − z0)α (32)

and that, for all s between α and 1,

u(s) ≡ f(s)

1− F (s)

(1− β)[δ2 − λφ2(z2 − z0)E(s|s ≥ s)]

βξ(1− F (s))−

λφ2(z2 − z0)[E(s|s ≥ s)− s]

(1 +

1− β

βξ

) > φ2(z2 − z0). (33)

These conditions are identical to (30) and (31) respectively when λ = 0. Increases in

λ lower the left hand side in both conditions and thereby increase the stringency of these

conditions.

31

If, in addition, ∫ 1

α[φ2(z2 − z0)s− p]dF (s) > 0 (34)

which requires that there exists a s < 1 such that

φ2(z2 − z0)s = p,

the firm benefits prefers setting λm equal to λα > 0 where

λα = βξφ2(z2 − z0)α− δ2

δ2(βξ + 1− β),

to setting λm = 0. The reason is that λm = λα allows for an equilibrium where s = α and

p = r + p.

Proof. Conditions (32) and (33) ensure that the minimum requirement curve is everywhere

above the maximum offer curve in the absence of manufacturer altruism. This means that,

even with a contractor whose altruism parameter equals λ, the equilibrium outcome involves

effort e0. When, instead, λm is given by λα, it follows immediately from (27) that the

manufacturer is willing to make offers for s ≥ α at price p + r. Given the expectation of

receiving offers at this price with probability one, (29) implies that the contractor is willing

to make effort e2. There is thus an equilibrium where the firm earns the left hand side of

(34) more than it does without altruism. The firm is thus willing to acquire this level of

altruism, particularly since the definition of λα implies that λα < 1. Q.E.D.

Altruism commits the manufacturer to lose money by paying p when s < s. For s near s,

the losses this occasions the manufacturer are small relative to the gains of the contractor, so

only a modest level of altruism is necessary to lead the manufacturer to offer p in this case.

What the manufacturer gains from this commitment is that his profits increase when s > s.

The reason this commitment is useful is that the manufacturer’s benefit from e2 when s = s,

φ2(z2 − z0)s, exceed its social cost δ2. The two parties thus have something to gain from

increasing the frequency of purchases and splitting the resulting surplus between them.17

17Altruism thus plays a similar role here as in Rotemberg and Saloner (1993) where altruism also allowsthe firm to earn increased profits on average by committing itself to earn lower profits in certain states ofnature where some other agent (in that case an employee with a particular prearranged incentive contract)gains greatly from the firm’s altruism.

32

The above proposition gives conditions under which the manufacturer prefers some al-

truism to selfishness when the latter gives rise to effort e0 in all states of demand. I now

show that this intuitive result holds also in situations where there already exist some states

of demand where the contractor makes effort e2. Such a situation can arise when (32) holds

but (33) fails to hold for at least some s between zero and one. An equilibrium like that

depicted in point A of Figure 3 can then exists. In this case

Proposition 9. Suppose the equilibrium with λm = 0 is interior so that 0 < s < 1. Ignoring

the costs of manufacturer altruism, the manufacturer gains by setting λm > 0 if (32) holds

and λ is sufficiently small that

δ2 > λφ2(z2 − z0)E(s|s ≥ s) + [E(s|s ≥ s)− s]

[1 +

βξ(1− F (s))

1− β

] (35)

for all s ≤ s

Proof. The effect of changing p and s on manufacturer profits can be obtained by differ-

entiating (28). This yields

dπm = −f(s)[φ2(z2 − z0)s− p + r

]ds−

(1− F (s)

)dp.

When λm = 0, (27) implies that the term in square brackets is zero. Thus profits are strictly

higher with λm > 0 if small increases in λm from λm = 0 lower p.

To understand why an increase in λm lowers p, note that the equilibrium must have

similar properties to those of point A in Figure 3. In particular, any interior equilibrium

must occur at a point where the maximum offer curve intersects the minimum requirement

curve from below. The reason is that, even if there is also an intersection from above, the

firm prefers points with lower values of p. The slope of the minimum requirement curve is

given by u(s), which is defined in (33). Thus this slope is positive at least until s if (35)

holds for all s ≤ s. Combined with (32), this implies that the intersection of the maximum

offer curve with the minimum requirement curve occurs at a price above δ2. As a result,

such an intersection takes place to the right of the point where the maximum offer curves for

different values of λ intersect. Thus an increase in λm from zero moves the equilibrium from

33

a point like A in Figure 3 to a point like B. In other words, it ensures that the maximum

offer curve with λm slightly higher than zero intersects the minimum requirement curve at a

lower value of p than does the maximum offer curve with λm = 0. Q.E.D.

The proposition shows that, if the equilibrium value of λ is relatively low, manufacturer

profits rise by increasing λm above zero. The reason is that this increases the range of

realizations of s such that the manufacturer offers p. For given p, the manufacturer loses

nothing from raising this range slightly. However, if λ is small enough, the contractor is

earning equilibrium rents so that the increase in this range allows the manufacturer to lower

p and this raises manufacturer profits.

4 Conclusion

This paper has shown that endogenous altruism can play a key role in determining whether

transactions take place inside or between firms. It can, in particular, lead to situations

where external suppliers engage in substantial effort to improve the quality of the product

they deliver. The suppliers that do so can be “trusted” by their customers. Moreover, the

model also predicts that buyers will sometimes respond to supplier altruism with altruism of

their own, so that trust becomes bidirectional. This fits, broadly, with an extensive literature

suggesting that vertical business relations in which firms trust each other are particularly

valuable (see Dyer and Chu 2003 for a recent example and many references). Most of this

empirical literature on trust does not measure the warmth of the feelings between individuals

in buying and selling organizations, however.18 It would thus be interesting to know the

extent to which these feelings are paramount among firms that have close relations with one

another.

One clear implication of the model is that these feelings need not always arise, nor does

18Smitka (1991) does not discuss these feelings explicitly either, His study stands out, however, because heemphasizes that trust between Japanese auto manufacturers and their suppliers required that the manufac-turers get to know the executives of the selling organizations personally (p. 169). He also suggests that socialactivities that included the engineers in both organizations contributed to an atmosphere of collaboration(p. 158-159).

34

any particular business have to have the same feelings for all those it deals with. It is easy to

imagine, for example, buyers purchasing inputs from different suppliers who vary in both the

extent to which they can increase quality through non-contractible actions and the extent

to which they find such actions costly. The model would then imply that a given buyer can

have quite different levels of altruism for different suppliers. Similarly, a particular supplier

may have different relations with different customers because their need for quality differs. In

addition, it is possible to interpret some of the equilibria I discussed in section 3 as involving

purchases from a selfish contractor when s is below s and purchases from an altruistic one

when s is above this cutoff. All of these re-interpretations of the model fit with Uzzi’s (1997)

observation that buyers and sellers typically have both “arm’s length” relations and “special”

ones, where only the latter correspond to altruistic ones. This variety in the relationships

of a single firm also serves to differentiate the model from genetic explanations for altruism

(as in Frank (1987)) as well as ones based on having had a common experience that has

permanently changed one’s tastes (as in Akerlof (1983)).

It is worth noting, however, that the analysis of multiple relationships is quite incomplete

in this model. A richer set of implications could also be drawn if the underlying parameters

of the model varied over time and if the time requirements for developing trusting relations

were made explicit. The model might then be able to rationalize the existence of firms with

different types of vertical relations at any given moment in time as well as the desire of

firms to change these relationships. It might also help explain why less integrated firms

can sometimes beat their integrated counterparts while, at other times, vertically integrated

firms appear impregnable.

35

References

Akerlof, George, “Loyalty Filters,” American Economic Review 73, March 1983, 54-63.

Baker, George, Robert Gibbons and Kevin J. Murphy, “Relational Contracts and theTheory of the Firm,” Quarterly Journal of Economics, 117, February 2002, 39-84.

Burt, Ronald S, and Marc Knez, “Trust and Third-Party Gossip,” in Roderick M. Kram-ner and Tom R. Tyler Trust in Organizations, Thousand Oaks: Sage, 1996.

Camerer, Colin, “Gifts as Economic Signals and Social Symbols,” American Journal ofSociology, 94, (supplement 1988), 675-700.

Carnevale, Peter J. D., Dean G. Pruitt and Patricia I. Carrington, “Effects of FutureDependence, liking, and Repeated Requests for Help on Helping Behavior,” SocialPsychology Querterly, 45, March 1982, 9-14.

Collins, Nancy L. and Lynn Carol Miller, “Self-disclosure and liking: A meta-analyticreview,” Psychological Bulletin, 116, November 1994, 457-475.

Dyer, Jeffrey H. and Wujin Chu, “The Role of Trustworthiness in Reducing TransactionCosts and Improving Performance: Empirical Evidence from the United States,Japan, and Korea,” Organization Science, 14, January-February 2003, 57-68.

Eccles, Robert G. and Harrison C. White, “Price and Authority in Inter-Profit CenterTransactions,” American Journal of Sociology, 94, 1988 Supplement, S17-S51.

Frank, Robert H. ”If Homo Economicus Could Choose His Own Utility Function, WouldHe Want One with a Conscience?” American Economic Review 77, September 1987,593-604.

Freeland, Robert F., The Struggle for Control of the Modern Corporation, Cambridge:Cambridge University Press, 2001.

Granovetter, Mark, “Economic Action and Social Structure: The Problem of Embedded-ness,” American Journal of Sociology, 91, 1985, 481-510.

Grossman, Sanford J. and Oliver D. Hart, “The Costs and Benefits of Ownership: Atheory of Vertical and Lateral Integration” Journal of Political Economy, August1986, 94, 691-719.

Homans, George, The Human Group, New York: Harcourt, 1950.

Ingram, Paul and Peter W. Roberts, “Friendships among Competitors in the Sydney

36

Hotel Industry, American Journal of Sociology, 106, September 2000, 387423.

Klein, Benjamin and Keith B. Leffler, “The Role of Market Forces in Assuring Contrac-tual Performance”, Journal of Political Economy, August 1981, 89, 615-41.

Kranton, Rachel E. and Deborah F. Minehart, “Networks versus Vertical Integration,”Rand Journal of Economics, Autumn 2000, 5, 301-31.

Levesque, Maurice, “Meta-Accuracy Among Acquainted Individuals: A Social RelationsAnalysis of Interpersonal Perception and Metaperception,” Journal of Personalityand Social Psychology, 72, January 1997, 66-74.

Lorenz, Edward H. “Neither Friends nor Strangers: Informal Networks of Subcontract-ing in French Industry,” in Gambetta, Diego ed. Trust: Making and BreakingCooperative Relations, New York: Basil Blackwell, 1988.

Radner, Roy, “Repeated Principal-agent Games with Discounting,” Econometrica, 53,September 1985, 1173-98.

Rotemberg, Julio J., “A Theory of Inefficient Intrafirm Transactions,” American Eco-nomic Review, 81, March 1991, 191-209.

—, “Human Relations in the Workplace,” Journal of Political Economy, 102, August1994, 684-718.

Rotemberg Julio J. and Garth Saloner, “Leadership Style and Incentives,” ManagementScience, 39, 1993, 1299-1318.

Rusbult, Caryl E.,“Satisfaction and commitment in friendships,” Representative Re-search in Social Psychology, 11, 1980, 96-105.

Simon, Herbert, “A Formal Theory Model of the Employment Relationship,” Economet-rica, 19, July 1951, 293-305.

Shapiro, Carl and Joseph E. Stiglitz, “Equilibrium Unemployment as a Worker Disci-plining Device,” American Economic Review, 74, June 1984, 433-44.

Smitka, Michael J., Competitive Ties: Subcontracting in the Japanese Automotive In-dustry, New York: Columbia University Press, 1991.

Uzzi, Brian, “Social Structure and Competition in Interfirm Networks: The Paradox ofEmbeddedness,” Administrative Science Quarterly, 42, March 1997, 35-67

Walker, Gordon and Laura Poppo, “Profit Centers, Single-Source Suppliers, and Trans-

37

actions Costs,” Administrative Science Quarterly, 36, March 1991, 66-87.

Wernerfelt, Birger, “On the Nature and Scope of the Firm: An Adjustment Cost Theory,”Journal of Business, 70, October 1997, 489-514.

38

Figure 1:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

0

2

4

6

8

10Maximum Offer Curves

λm=0

λm=.2

s

p

39

Figure 2:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14Minimum Requirement Curves

λ=0

λ=.2

s

p

40

Figure 3:

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

0

2

4

6

8

10

12

14Benefit of Marginal Increases in Manufacturer Altruism

λm=0λm=.2

A

B

s

p

41